Department Seminar 2014
Title: Algorithmic models of market equilibrium
Speaker: Vladimir Shikhman from Catholic University of Louvain, Belgium
Abstract: This talk deals with mathematical modeling of economic markets towards their algorithmic nature. The focus lies on the reasonable dynamic adjustment processes converging to a market equilibrium. Our goal is to reveal the behaviour and price dynamics of market participants given by tractable algorithmic procedures. For that, we suggest a new framework for contructing mathematical models of market activity. Contrary to the majority of the classical economical models, we get a characterization of general equilibrium of the market as a saddle point in a convex-concave game. This feature significantly simplies the proof of existence theorems and construction of the adjustment processes both for producers and consumers. Moreover, we argue that the unique equlibrium prices can be characterized as a unique limiting point of some simple price dynamics. In our model, the equilibrium prices have natural explanation: They minimize the total excessive revenue of the market's participants. Due to convexity, all our adjustments processes have unambiguous behavioral and algorithmic interpretation, in addition, their computational complexity can be estimated.
In collaboration with Yu. Nesterov
Title: Integrating different modeling approaches in systems biology
Speaker: Ursula Kummer
Abstract: Computional models of biological processes play an important role in modern bioscientific research. In particular fields like systems biology and synthetic biology heavly rely on the support by computational means. The vast majority of models only describe a certain level of abstraction, e.g. cellular processes or the behaviour of cells as a whole within a tissue or the distribution of substances in the blood stream of a whole body. Obviously, it would be beneficial to bridge these different levels of abstraction thereby integrating knowledge. With the example of the impact of interferon in hepatitis C therapy, I will discuss the state-of-the-art in computational modeling at different levels of abstraction and the first step towards an integration of these levels.
Title: Computational Medicine - Opportunities and challenges
Speaker: Prof. Arvid Lundervold, MD, PhD, UiB's Department of Biomedicine, Neuroinformatics and Image Analysis Laboratory
Abstract: Computational medicine (CM) is a new field of science that can be defined as the application of methods from engineering, mathematics and computional sciences to improve our understanding and treatment of human diseases. In this talk, I will give a short glimpse of this exciting and increasingly important field where informatics and computer science play key roles. CM is characterized by being multi-scale (molecule to man, microseconds to year), sub-specialized (e.g. computational anatomy, computational cardiology, computational radiology), often dealing with multidimensional big data and high-content, highthrhoughput data acqusition instruments, employing an impressive range of mathematical and statistical methods (e.g. differential geometry, graph theory, machine learning), and having a huge potential within personalized medicine, disease prevention and therapy. Some examples from recent CM applications will be given and collaborative opportunities within the cross-discipllinary MedViz research network here in Bergen will be presented.
Title: Working with objects - in computer and mind
Speaker: Trygve Reenskaug
Abstract: I introduce a new paradigm for computer programming called DCI - Data, Context, Interaction. DCI brings programming to the level of everyday concepts and activities. The professional programmer can attack complex problems without undue additional complexity. The software maintainer can preserve system integrity by understanding and honoring the system architecture long after the originators have moved on to other projects. DCI can be embedded in different programming languages that are specialized for different purposes. The DCI concepts can become a unifying foundation for programming. DCI specifies a program as seen in two orthogonal projections; the Data projection describes system state and the Context projection system behavior.
Title: CONCURRENT REACHABILITY GAMES: TO PURGATORY AND BACK
Speaker: Petter Bro Miltersen, Aarhus University
Abstract There are seven terraces in Purgatory, indexed 1,2,3,4,5,6,7. Dante enters Purgatory at terrace 1. Each day, if Dante finds himself at some terrace i, he must play a game of matching pennies against Lucifer: Lucifer hides a penny, and Dante must try to guess if it is heads up or tails up. If Dante guesses correctly, he proceeds to terrace i+1 the next morning — if i-1 is 8, he enters Paradise and the game ends. If, on the other hand, Dante guesses incorrectly, there are two cases. If he incorrectly guesses “heads”, he goes back to terrace 1 the next morning. If he incorrectly guesses "tails" the game ends and Dante forever loses the opportunity of visiting Paradise. How can Dante ensure ending up in Paradise with probability at least 3/4? How long should he expect to stay in Purgatory before the game ends in order to achieve this?
We solve the riddle (which is joint work with Hansen and Koucky) and uncover its connections to seemingly unrelated areas of mathematics and computer science, including formal verification, algorithms, and real algebraic geometry.